Unit 6 (Modeling Equivalent Fractions)

Hi there!  On Tuesday, students took the Unit 5 test.  We began Unit 6 on Wednesday.  Unit 6 focuses on Fraction Equivalence and Comparison.  We are building on student's fraction knowledge from 3rd grade. Please view the parent flyer/video for this upcoming unit.  It is such a great resource provided by the Hillsborough County Math Department! http://www1.sdhc.k12.fl.us/~elementarymath/CCSSMGCG13/4/parent/u6.pdf

We spent the 1st couple days of this unit creating concrete models with fraction strips and area models to model fractions as parts of a region and to find equivalent fractions. Students will transition from using models to using multiplication to generate equivalent fractions.

Day 1 (Weds, Dec. 3)-    How can you model equivalent fractions with an area model?

We began this lesson with the following problem.

We discussed the problem as whole group before students solved.  We talked a lot about what the numerator and denominator represented in this problem.  I showed students the following blank chart of 3/9.

We discussed what the 9 (the denominator) represented in this problem.  It represented the amount of equal parts that the field (the whole) was divided/broken into.  We then had a discussion about the 3 (the numerator) in the problem.  Students decided that the 3 represented the 3 equal parts (out of the 9) where the horses were kept. From there, I had students develop their own definitions of the numerator and denominator.  As a class, we came up with the following definitions below.  I have to say I was impressed! The numerator is the # above the bar in a fraction.  It tells how many parts of the whole we're working with/ or are being considered.  The denominator is the # below the bar in a fraction.  It tells how many parts are in the whole or group. When working with your child, please have them explain what the numerator and denominator represents in each problem.

Below you will find the different ways in which students chose to solve the problem.  Each of these students shared their thinking with the class!
This student used grid paper to draw a model for 3/9 and then drew another model and divided it into thirds. She was able to prove that 3/9 is equivalent to 1/3.

This student drew an area model to prove that 6/18 is equivalent to 3/9.

This student drew an area model to prove that 3/9, 1/3, and 2/6 are all equivalent!

Proving that 3/9 is equivalent to 2/6.

 Proving that 3/9 is equal to 5/15.

Area models are great tools for finding equivalent fractions.  However, students must make sure that they are breaking their models into equal parts and that the wholes are the same size!  The purpose of area models is to build student's conceptual understanding of equivalent fractions.  The goal is to transition students from models to using multiplication to generate equivalent fractions, however they must see the connection first!

Day 2/ 3- How can you model equivalent fractions with a linear model?

Students were presented with the following problem and were provided with a sentence strip to aid them in solving the problem.  It was awesome to see all of the ways students used the strip/linear models to solve this problem.  

This student drew 2 linear models to represent 2/4 and 3/8.  He was able to prove that they are not equivalent and that 2/4 (Savannah's amount) is larger.  He even said that Lin would need 1/8 more to have the same as Savannah! Awesome! The student also mentioned that they knew 2/4 is equal to 1/2 and that 3/8 would be less than 1/2 because you would need 4/8 to equal 1/2!  LOVE it!

This student folded their strip into fourths and shaded in 2 of the fourths to represent Lin's amount (2/4).  Then the folded the bottom part into eights and shaded in 3 of them to represent Lin's amount (3/8).  Based on the student's model, they were able to explain that they were not equal!

This student drew a number line, which is a type of helpful linear model to also prove that 3/8 and 2/4 are not equivalent.

Look at this student also using a number line to prove to the class that 2/4 and 3/8 are not equivalent.

Next, each team was assigned 2 fractions and they had to decide if they were equivalent or not using linear models! 

Here is preview of this upcoming week in math:

Monday 12/8- Tropicana Speeches/ finish linear models lesson on equivalent fractions

Tuesday 12/9- How can you use multiplication to generate equivalent fractions?

Wednesday 12/10- How can you use equivalent fractions to help you find common denominators?

Thursday 12/11- What strategies can you use to record fractions in simplest form?

Friday 12/12- Field Trip

If you ever have any questions regarding what your child is learning in math, please don't hesitate to ask!  Thank you for your help at home!